Grades 9-10 Video Solutions 2010-Levels 9&10 Video Solutions 2010 problem30

Levels 9&10 Video Solutions 2010 problem30

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Video Summary

The problem involves calculating the number of barcodes possible with a set width of 12, composed of alternating black and white stripes, with each having a width of either 1 or 2 units. Since barcodes must have an odd number of stripes, the width can be partitioned into 11, 9, or 7 strips. The combinations are calculated using combinations formula, giving 11 choose 1, 9 choose 3, and 7 choose 5 for possible layouts. Summing these gives a total of 116 barcodes, concluding that 116 unique barcode arrangements are possible with these criteria.

Keywords

barcode calculation

stripe combinations

alternating stripes

width partitioning

unique arrangements